Analysis and design of a cryostat which functions in space by radiative cooling alone are presented. Temperatures in the inner volume of the cryostat are predicted to reach cryogenic temperatures if the cryostat is placed in an earth orbit in the plane of the ecliptic. The advantages of the cryostat include (1) indefinitely long lifetime, (2) no cryogenic or heat pump plant as payload, and (3) the use of certain radio wave, millimeter wave, and infrared detectors. A parametric analysis of various cryostat configurations has been completed to allow solution of design parameters for various applications, earth orbital radii, and internal heat loads.